15-odd-limit: Difference between revisions
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This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized [[ | This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized [[edo]]s (~15 to 41 steps). | ||
* [[1/1]] | * [[1/1]] | ||
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The smallest edo which is consistent in the 15-odd-limit is [[29edo]]. | |||
The one that is distinctly consistent in the same is [[111edo]]. | |||
== See also == | == See also == | ||
* [[Arto and | * [[Arto and tendo theory]] | ||
* [[Diamond15]] – as a scale | |||
[[Category:15-odd-limit| ]] <!-- main article --> | [[Category:15-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 13:45, 8 October 2025
The 15-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 15 and k is an integer. To the 13-odd-limit, it adds 4 pairs of octave-reduced intervals involving 15.
Below is a list of all octave-reduced intervals in the 15-odd-limit. This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized edos (~15 to 41 steps).
- 1/1
- 16/15, 15/8
- 15/14, 28/15
- 14/13, 13/7
- 13/12, 24/13
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 8/7, 7/4
- 15/13, 26/15
- 7/6, 12/7
- 13/11, 22/13
- 6/5, 5/3
- 11/9, 18/11
- 16/13, 13/8
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 13/10, 20/13
- 4/3, 3/2
- 15/11, 22/15
- 11/8, 16/11
- 18/13, 13/9
- 7/5, 10/7
| Ratio | Size (¢) | Color name | Name(s) | |
|---|---|---|---|---|
| 16/15 | 111.731 | g2 | gu 2nd | classic diatonic semitone |
| 15/14 | 119.443 | ry1 | ruyo unison | septimal diatonic semitone |
| 15/13 | 247.741 | 3uy2 | thuyo 2nd | tridecimal supermajor second / tridecimal second-third |
| 15/11 | 536.951 | 1uy4 | luyo 4th | undecimal acute fourth |
| 22/15 | 663.049 | 1og5 | logu 5th | undecimal grave fifth |
| 26/15 | 952.259 | 3og7 | thogu 7th | tridecimal subminor seventh / tridecimal sixth-seventh |
| 28/15 | 1080.557 | zg8 | zogu octave | small septimal major seventh |
| 15/8 | 1088.269 | y7 | yo 7th | just major seventh |
The smallest edo which is consistent in the 15-odd-limit is 29edo.
The one that is distinctly consistent in the same is 111edo.
See also
- Arto and tendo theory
- Diamond15 – as a scale